Sleep is the greatest thief. It steals half of our lives.
Literal
Sleep [topic-は] greatest thief. Life [possessive-の] half [even-も] steal-[completely-しまう].
最大 = 'the greatest.' 盗んでしまう uses ~てしまう for completive/emphatic steal — 'goes and steals.' も adds 'even' to the half of life. A melodramatic observation on the time sleep takes from us.